The θ-Field Between Electric and Magnetic Fields as a Fundamental Variable of Space-Time: Geodesics, Light Deflection, Cosmological Extension, and Numerical Constraints — Version 11

This speculative preprint presents Version 11 of the θ-field framework, a proposed electromagnetic scalar-gravity candidate in which the angle θ between electric and magnetic field vectors is treated as a dynamic Lorentz-scalar field θ(x). Within the framework, gravitational behaviour is associated with spatial gradients of θ, while the standard electromagnetic vacuum is recovered as the limiting condition θ → 90°. Version 11 consolidates previous developments and adds the first numerical cosmological results. The manuscript includes a regularised Lorentz-covariant definition of the θ-field with the regularisation scale fixed at the Planck length, an effective Lagrangian, a full stress-energy coupling, a derivation of the Newtonian weak-field limit, test-particle geodesics, and an explicit solar light-deflection calculation yielding 1.7505 arcsec in the β₂ = 0 limit. It also discusses the quantum extension, Ward identities, ghost decoupling in Lorenz gauge, and a structured list of remaining QFT and gravitational open problems. A central update inherited from v10.1 is the partial resolution of OP-GR-1 through Sakharov induced gravity. Under a Planck-scale proper-time cutoff and an effective field theory truncation to dimension-four operators, the one-loop θ-field path integral induces an Einstein-like gravitational action, with the non-minimal coupling fixed by the matching condition ξ = 1/6 − 1/(2π) ≈ 0.0076. This result is explicitly presented as scheme-dependent at one loop and not as a complete derivation of general relativity. The main new contribution of Version 11 is the numerical integration of the FLRW-θ coupled system for several values of the coupling β using Planck 2018 cosmological parameters. These calculations provide θ₀(z) profiles across cosmic history, the first quantitative constraints on the θ-photon polarisation coupling αc from CMB birefringence bounds, and a numerical resolution of the Mercury perihelion-precession test within the slow-roll regime. The paper identifies CMB EB/TB polarisation correlations, EHT polarimetry, and future LiteBIRD measurements as relevant observational tests. This work is not peer-reviewed and does not claim to establish a completed theory of gravity. It is presented as a falsifiable speculative research programme with explicit separation between derived results, phenomenological extensions, numerical constraints, and open problems.